Chapter 33, Problem 78 In about A.D. 150, Claudius Ptolemy gave the following (b

Question

Chapter 33, Problem 78 In about A.D. 150, Claudius Ptolemy gave the following (below) measured values for the angle of incidence 8 and the angle of refraction 82 for a light beam passing from air to water. Assuming these data are consistent with the law of refraction, use them to find the index of refraction of water. These data are interesting as perhaps the oldest recorded physical measurements. Assume that the index of refraction of air under standard temperature (0 degree C) and pressure (1 atm) is 1.00029. Number Units

Explanation / Answer

a doubling of the angle of incidence from 40 degrees to 80 degrees does not result in a doubling of the angle of refraction. Thus, a plot of this data would not yield a straight line

on plotting the graph between their Sine angle alues, we find a straight line

it could be written as y= m*x + b

so Sine ?1 = 1.33 x sine ?2 + 0.00

now index of refraction of the material (n)

n = Sine (?1) / sine (?2)

using this equation we get

n = 1.00029.

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